1/r² is for an isotropic radiator, but Voyager 1 mounts (thankfully) a high gain directional antenna. The antenna gains seems 36dBi or 48dBi, depending on the frequency [1]. This means that when pointed towards Earth, the signal power is actually between 4000 to 63000 times stronger than what that formula would give you. It's still tiny, but not as bad as that would suggest.
No, it is for any radiator. The gain of the antennas has absolutely nothing to do with the pathloss, it just changes the radiated power or the concentration effect of the antenna because of antenna related gains. Every kind of antenna has its own specific gain and corresponding losses diagram based on which way the source is relative to the antenna, with the baseline being an omnidirectional radiator (which no antenna really is, but we assume it is).
Well, consider that the speed of light itself is pretty slow, relative to what people's perception of the speed of light is. Even if you had a spaceship traveling at 99.99%, it'd take a surprisingly long time even to reach the Oort cloud.
A month or so for you. Enough time to catch up on a few favorite shows and finish a few books. Now if anyone is waiting for you on earth, they will wait considerably longer
Actually - to reach the start of the Oort Cloud from Earth it'd take around 4 hours. That's 2000 AU. The observer on Earth will see it as about 12 days. This is assuming 99.99% of the speed of light which is completely unrealistic of course.
And the closest known galaxy to the Milky Way, Canis Major Dwarf Galaxy, is just 25,000 light-years away - it's almost incomprehensible how fast the universe is!
> the spacecraft, in flight since 1977, is cruising at nearly 38,000 mph (61,000 kph) through the vacuum of space,
The page takes great pains to explain things, but omits a frame of reference for this speed. I’m guessing it’s sun-relative, but it could be relative to its take-off on Earth. Does anyone know?
Checked my bot's post from earlier today (taken from NASA's data[0]) and it says "Velocity relative to the Earth is about 34 km/sec (~77,173 mph); to the Sun about 16 km/sec (~37,763 mph.)"
You're right that Earth is catching up to the Voyagers during part of its orbit for several months in the early part of the year (and you'll see that reflected on the Mission Status page). Consequently I used to wonder if Voyager 1 would reach 1 light day from Earth 3 times - the first time, then a second time when the Earth distance decreased, and then a third time when distance increased again!
If you scroll down on this TheSkyLive page, you can see a graph of Voyager 1's distance from Earth over time and it's an up-sloping ripple instead of a straight line. You can play with the markers to zoom in and see that the catch-up phase happens in the early part of the year:
I know it's a joke but it's because there's no clearly defined end of the solar system.
Just re-reading Pale Blue Dot by Carl Sagan and he talks about this. If we define the end of the solar system as the point where the suns gravity no longer holds, then it's going to be a very long time for it to escape the solar system.
I'm going to go find that passage in the book. Hopefully I can find it before the edit window closes for this comment.
I'm just going to repost stuff from my blog about the Voyager space probes. I've posted this here before -
The two Voyager spacecraft are the greatest love letters humanity has ever sent into the void.
Voyager 2 actually launched first, on August 20, 1977, followed by Voyager 1 on September 5, 1977. Because Voyager 1 was on a faster, shorter trajectory (it used a rare alignment to slingshot past both Jupiter and Saturn quicker), it overtook its twin and became the farther, faster probe. As of 2025, Voyager 1 is the most distant human-made object ever, more than 24 billion kilometers away, still whispering data home at 160 bits per second.
Each spacecraft carries an identical 12-inch gold-plated copper phonograph record.
The contents:
- Greetings in 55 human languages.
- A message from UN Secretary-General at the time and one from U.S. President Jimmy Carter.
- 115 analog images encoded in the record’s grooves: how to build the stylus and play the record, the solar system’s location using 14 pulsars as galactic GPS, diagrams of human DNA, photos of a supermarket, a sunset, a fetus, people eating, licking ice cream, and dancing
The record is encased in an aluminum jacket with instructions etched on the cover: a map of the pulsars, the hydrogen atom diagram so aliens can decode the time units, and a tiny sample of uranium-238 so they can carbon-date how old the record is when they find it.
Sagan wanted the record to be a message in a bottle for a billion years. The spacecraft themselves are expected to outlive Earth. In a billion years, when the Sun swells into a red giant and maybe swallows Earth, the Voyagers will still be cruising the Milky Way, silent gold disks carrying blind, naked humans waving hello to a universe that may never wave back.
And it was Sagan who, in 1989, when Voyager 1 was already beyond Neptune and its cameras were scheduled to be turned off forever to save power, begged NASA for one last maneuver. On Valentine’s Day 1990, the spacecraft turned around, took 60 final images, and captured Earth as a single pale blue pixel floating in a scattered beam of sunlight — the photograph that gives the book its name and its soul.
It was the photograph that inspired this famous quote -
"Look again at that dot. That's here. That's home. That's us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every "superstar," every "supreme leader," every saint and sinner in the history of our species lived there-on a mote of dust suspended in a sunbeam.
The Earth is a very small stage in a vast cosmic arena. Think of the endless cruelties visited by the inhabitants of one corner of this pixel on the scarcely distinguishable inhabitants of some other corner, how frequent their misunderstandings, how eager they are to kill one another, how fervent their hatreds. Think of the rivers of blood spilled by all those generals and emperors so that, in glory and triumph, they could become the momentary masters of a fraction of a dot.
Our posturings, our imagined self-importance, the delusion that we have some privileged position in the Universe, are challenged by this point of pale light. Our planet is a lonely speck in the great enveloping cosmic dark. In our obscurity, in all this vastness, there is no hint that help will come from elsewhere to save us from ourselves.
The Earth is the only world known so far to harbor life. There is nowhere else, at least in the near future, to which our species could migrate. Visit, yes. Settle, not yet. Like it or not, for the moment the Earth is where we make our stand...
I wish we actually did things quickly instead of taking forever and having 1 million ethical issues about everything. We know how to get close to light speed. You can just explode nuclear bombs behind you. Why don’t we do it?
35 comments
[ 0.19 ms ] story [ 35.4 ms ] thread[1]: https://space.stackexchange.com/questions/65801/what-are-the...
The page takes great pains to explain things, but omits a frame of reference for this speed. I’m guessing it’s sun-relative, but it could be relative to its take-off on Earth. Does anyone know?
[0] https://eyes.nasa.gov/assets/dynamic/dynamo/sc_voyager_1/now...
https://science.nasa.gov/mission/voyager/where-are-voyager-1...
You're right that Earth is catching up to the Voyagers during part of its orbit for several months in the early part of the year (and you'll see that reflected on the Mission Status page). Consequently I used to wonder if Voyager 1 would reach 1 light day from Earth 3 times - the first time, then a second time when the Earth distance decreased, and then a third time when distance increased again!
If you scroll down on this TheSkyLive page, you can see a graph of Voyager 1's distance from Earth over time and it's an up-sloping ripple instead of a straight line. You can play with the markers to zoom in and see that the catch-up phase happens in the early part of the year:
https://theskylive.com/voyager1-info
https://theskylive.com/voyager2-info
[1] https://xkcd.com/1189/
I know it's a joke but it's because there's no clearly defined end of the solar system.
Just re-reading Pale Blue Dot by Carl Sagan and he talks about this. If we define the end of the solar system as the point where the suns gravity no longer holds, then it's going to be a very long time for it to escape the solar system.
I'm going to go find that passage in the book. Hopefully I can find it before the edit window closes for this comment.
Voyager 2 actually launched first, on August 20, 1977, followed by Voyager 1 on September 5, 1977. Because Voyager 1 was on a faster, shorter trajectory (it used a rare alignment to slingshot past both Jupiter and Saturn quicker), it overtook its twin and became the farther, faster probe. As of 2025, Voyager 1 is the most distant human-made object ever, more than 24 billion kilometers away, still whispering data home at 160 bits per second.
Each spacecraft carries an identical 12-inch gold-plated copper phonograph record.
The contents:
- Greetings in 55 human languages.
- A message from UN Secretary-General at the time and one from U.S. President Jimmy Carter.
- 115 analog images encoded in the record’s grooves: how to build the stylus and play the record, the solar system’s location using 14 pulsars as galactic GPS, diagrams of human DNA, photos of a supermarket, a sunset, a fetus, people eating, licking ice cream, and dancing
The record is encased in an aluminum jacket with instructions etched on the cover: a map of the pulsars, the hydrogen atom diagram so aliens can decode the time units, and a tiny sample of uranium-238 so they can carbon-date how old the record is when they find it.
Sagan wanted the record to be a message in a bottle for a billion years. The spacecraft themselves are expected to outlive Earth. In a billion years, when the Sun swells into a red giant and maybe swallows Earth, the Voyagers will still be cruising the Milky Way, silent gold disks carrying blind, naked humans waving hello to a universe that may never wave back.
And it was Sagan who, in 1989, when Voyager 1 was already beyond Neptune and its cameras were scheduled to be turned off forever to save power, begged NASA for one last maneuver. On Valentine’s Day 1990, the spacecraft turned around, took 60 final images, and captured Earth as a single pale blue pixel floating in a scattered beam of sunlight — the photograph that gives the book its name and its soul.
It was the photograph that inspired this famous quote -
"Look again at that dot. That's here. That's home. That's us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every "superstar," every "supreme leader," every saint and sinner in the history of our species lived there-on a mote of dust suspended in a sunbeam.
The Earth is a very small stage in a vast cosmic arena. Think of the endless cruelties visited by the inhabitants of one corner of this pixel on the scarcely distinguishable inhabitants of some other corner, how frequent their misunderstandings, how eager they are to kill one another, how fervent their hatreds. Think of the rivers of blood spilled by all those generals and emperors so that, in glory and triumph, they could become the momentary masters of a fraction of a dot.
Our posturings, our imagined self-importance, the delusion that we have some privileged position in the Universe, are challenged by this point of pale light. Our planet is a lonely speck in the great enveloping cosmic dark. In our obscurity, in all this vastness, there is no hint that help will come from elsewhere to save us from ourselves.
The Earth is the only world known so far to harbor life. There is nowhere else, at least in the near future, to which our species could migrate. Visit, yes. Settle, not yet. Like it or not, for the moment the Earth is where we make our stand...
No message you send out ever gets far enough for anyone to see it. No ship you send out ever reaches another system. It’s just a big empty void.
You stay in your own lame system, browsing lame terrestrial memes and never escape.
Yes, that is one of the hypothesis